scholarly journals m-Polar Generalization of Fuzzy T-Ordering Relations: An Approach to Group Decision Making

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 51
Author(s):  
Azadeh Zahedi Khameneh ◽  
Adem Kilicman
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Fuzzy Data ◽  
Fuzzy Relations ◽  
Ranking Problem ◽  
Finite Case ◽  
Aggregation Functions ◽  
Infinite Case ◽  
Fuzzy Setting ◽  
Minimum Operator

Recently, T-orderings, defined based on a t-norm T and infimum operator (for infinite case) or minimum operator (for finite case), have been applied as a generalization of the notion of crisp orderings to fuzzy setting. When this concept is extending to m-polar fuzzy data, it is questioned whether the generalized definition can be expanded for any aggregation function, not necessarily the minimum operator, or not. To answer this question, the present study focuses on constructing m-polar T-orderings based on aggregation functions A, in particular, m-polar T-preorderings (which are reflexive and transitive m-polar fuzzy relations w.r.t T and A) and m-polar T-equivalences (which are symmetric m-polar T-preorderings). Moreover, the construction results for generating crisp preference relations based on m-polar T-orderings are obtained. Two algorithms for solving ranking problem in decision-making are proposed and validated by an illustrative example.

GÖDEL REPRESENTABLE FUZZY WEAK ORDERS

1999 ◽  
Vol 07 (02) ◽  
pp. 135-153 ◽  
Author(s):  
BERNARD DE BAETS ◽  
JÁNOS FODOR ◽  
ETIENNE KERRE
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Numerical Evaluation ◽  
Group Decision ◽  
Finite Family ◽  
Numerical Representation ◽  
Fuzzy Relations ◽  
Minimum Operator ◽  
Weak Orders

This paper is devoted to the study of fuzzy weak orders, fuzzy quasi orders and fuzzy quasi-transitive relations in the context of group decision making. Transitivity is modelled by means of the minimum operator. In analogy to the numerical representation of classical weak orders, we consider a particular class of fuzzy weak orders that can be constructed from a numerical evaluation by means of Gödel implicator. We fully characterize the fuzzy relations that can be written as the intersection or union of a finite family of these so-called Gödel representable fuzzy weak orders.

A Formal Approach to Handling Conflicts in Multiattribute Group Decision Making

2005 ◽  
Vol 128 (4) ◽  
pp. 678-688 ◽  
Author(s):  
Tung-King See ◽  
Kemper Lewis
Keyword(s):  
Decision Making ◽  
Engineering Design ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Problems ◽  
Team Leaders ◽  
Formal Approach ◽  
Aggregation Functions ◽  
Group Members ◽  
Problem Data

Supporting the decision of a group in engineering design is a challenging and complicated problem when issues like consensus and compromise must be taken into account. In this paper, we present the foundations of the group hypothetical equivalents and inequivalents method and two fundamental extensions making it applicable to new classes of group decision problems. The first extension focuses on updating the formulation to place unequal importance on the preferences of the group members. The formulation presented in this paper allows team leaders to emphasize the input from certain group members based on experience or other factors. The second extension focuses on the theoretical implications of using a general class of aggregation functions. Illustration and validation of the developments are presented using a vehicle selection problem. Data from ten engineering design groups are used to demonstrate the application of the method.

scholarly journals NEW GROUP DECISION MAKING METHOD IN INTUITIONISTIC FUZZY SETTING BASED ON TOPSIS

2015 ◽  
Vol 23 (3) ◽  
pp. 441-461 ◽  
Author(s):  
Wei YANG ◽  
Zhiping CHEN ◽  
Fang ZHANG
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Order Preference ◽  
Topsis Technique ◽  
Fuzzy Group Decision Making ◽  
Fuzzy Setting

In multiple attribute group decision making, the weights of decision makers are very crucial to ranking results and have gained more and more attentions. A new approach to determining experts’ weights is proposed based on the TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method in intuitionistic fuzzy setting. The weights determined by our method have two advantages: the evaluation value has a large weight if it is close to the positive ideal evaluation value and far from negative ideal evaluation values at the same time, otherwise it is assigned a small weight; experts have different weights for different attributes, which are more appropriate for real decision making problems since each expert has his/her own knowledge and expertise. The multiple attribute intuitionistic fuzzy group decision making algorithm has been proposed which is suitable for different situations about the attribute weight information, including the attribute weights are known exactly, partly known and unknown completely. A supplier selection problem and the evaluation of murals in a metro line are finally used to illustrate the feasibility, efficiency and practical advantages of the developed approaches.

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